Adaptive equalizers are known for compensating for impairments which are unpredictable or time-varying. Such equalisers are adapted by generating coefficients based on the current conditions, typically from the inputs and/or outputs of the equalizer. The coefficients are then used typically by carrying out a convolution with the equalizer inputs. Many algorithms are known for generating suitable coefficients, and adapting them to converge iteratively towards an optimum compensation. In some cases known training inputs can be used, in other cases it is more practical if the algorithm can converge without needing known inputs, known as blind equalization. Such equalization can be used in a receiver for compensating for impairments introduced in a transmission channel, or for other applications such as filtering of signals from a sensor.
In a receiver, to enable higher transmission capacity over an optical fiber, coherent detection has recently enabled high-order modulation formats in single-carrier (SC) optical systems where a simple feed-forward equalizer (FFE), in proper configuration, is able to compensate for fiber linear impairments, such as group velocity dispersion (GVD) and polarization mode dispersion (PMD). This has been shown by G. Colavolpe, T. Foggi, E. Forestieri, and G. Prati, “Robust multilevel coherent optical systems with linear processing at the receiver,” J. Lightwave Tech., vol. 27, pp. 2357-2369, Jul. 1, 2009, (hereinafter Colavolpe et al) using asynchronous detection in the form of a non coherent sequence detection to track phase changes in the channel.
The convergence of the iterative generation of coefficients for equalization of systems using QAM signals in polarization multiplexed coherent optical systems is not as straightforward as it is with QPSK modulation formats. There exist several different solutions, from the simple constant modulus algorithm (CMA) to more complicated versions of the CMA itself, like the radius directed equalizer (RDE), which trade between effectiveness and complexity. However, such blind algorithms may drive the convergence to local minima of the error function, so that the best performance of the linear equalizer cannot be reached. Thus, with existing algorithms a fast and reliable convergence is not guaranteed.